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October, 2019 Hardy and Rellich inequalities with exact missing terms on homogeneous groups
Duy Tuan NGUYEN, Nguyen LAM-HOANG, Triet Anh NGUYEN
J. Math. Soc. Japan 71(4): 1243-1256 (October, 2019). DOI: 10.2969/jmsj/80878087


We prove several identities on homogeneous groups that imply the Hardy and Rellich inequalities for Bessel pairs. These equalities give a straightforward understanding of some of the Hardy and Rellich inequalities as well as the absence of nontrivial optimizers and the existence/nonexistence of “virtual”extremizers.

Funding Statement

The second author (the corresponding author) was partially supported by a fellowship from the Pacific Institute for the Mathematical Sciences.


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Duy Tuan NGUYEN. Nguyen LAM-HOANG. Triet Anh NGUYEN. "Hardy and Rellich inequalities with exact missing terms on homogeneous groups." J. Math. Soc. Japan 71 (4) 1243 - 1256, October, 2019.


Received: 14 July 2018; Published: October, 2019
First available in Project Euclid: 13 June 2019

zbMATH: 07174405
MathSciNet: MR4023306
Digital Object Identifier: 10.2969/jmsj/80878087

Primary: 22E30
Secondary: 26D10 , 43A80 , 43A85

Keywords: Bessel pair , Hardy inequality , Hardy–Rellich inequality , homogeneous Lie group , remainder term

Rights: Copyright © 2019 Mathematical Society of Japan


Vol.71 • No. 4 • October, 2019
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